Science, culture, complexity

Tag: David Thouless

  • Majorana 1, science journalism, and other things

    While I have many issues with how the Nobel Prizes are put together as an institution, the scientific achievements they have revealed have been some of the funnest concepts I’ve discovered in science, including the clever ways in which scientists revealed them. If I had to rank them on this metric, the first place would be a tie between the chemistry and the physics prizes of 2016. The chemistry prize went to Jean-Pierre Sauvage, Fraser Stoddart, and Ben Feringa for “for the design and synthesis of molecular machines”. Likewise, the physics prize was shared between David Thouless, Duncan Haldane, and John Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter”. If you like, you can read my piece about the 2016 chemistry prize here. A short excerpt about the laureates’ work:

    … it is fruitless to carry on speculating about what these achievements could be good for. J. Fraser Stoddart, who shared the Nobel Prize last year with Feringa for having assembled curious molecular arrangements like Borromean rings, wrote in an essay in 2005, “It is amazing how something that was difficult to do in the beginning will surely become easy to do in the event of its having been done. The Borromean rings have captured our imagination simply because of their sheer beauty. What will they be good for? Something for sure, and we still have the excitement of finding out what that something might be.” Feringa said in a 2014 interview that he likes to build his “own world of molecules”. In fact, Stoddart, Feringa and Jean-Pierre Sauvage shared the chemistry prize for having developed new techniques to synthesise and assemble organic molecules in their pursuits.

    In the annals of the science Nobel Prizes, there are many, many laureates who allowed their curiosity about something rather than its applications to guide their research. In the course of these pursuits, they developed techniques, insights, technologies or something else that benefited their field as a whole but which wasn’t the end goal. Over time the objects of many of these pursuits have also paved the way for some futuristic technology themselves. All of this is a testament to the peculiar roads the guiding light of curiosity opens. Of course, scientists need specific conditions of their work to be met before they can commitment themselves to such lines of inquiry. For just two examples, they shouldn’t be under pressure to publish papers and they shouldn’t have to worry about losing their jobs if they don’t file patents. I can also see where the critics of such blue-sky research stand and why: while there are benefits, it’s hard to say ahead of time what they might be and when they might appear.

    This said, the work that won the 2016 physics prize is of a similar nature and also particularly relevant in light of a ‘development’ in the realm of quantum computing earlier this month. Two of the three laureates, Thouless and Kosterlitz, performed an experiment in the 1970s in which they found something unusual. To quote from my piece in The Hindu on February 23:

    If you cool some water vapour, it will become water and then ice. If you keep lowering the temperature until nearly absolute zero, the system will have minimal thermal energy, allowing quantum states of matter to show. In the 1970s, Michael Kosterlitz and David Thouless found that the surface of superfluid helium sometimes developed microscopic vortices that moved in pairs. When they raised the temperature, the vortices decoupled and moved freely. It was a new kind of … phase transition: the object’s topological attributes changed in response to changes in energy [rather than it turning from liquid to gas].

    The findings here, followed by many others that followed, together with efforts by physicists to describe this new property of matter using mathematics, in harmony with other existing theories of nature all laid the foundation for Microsoft’s February 19 announcement: that it had developed a quantum-computing chip named Majorana 1 with topological qubits inside. (For more on this, please read my February 23 piece.) Microsoft has been trying to build this chip since at least 2000, when a physicist then on the company’s payroll named Alexei Kitaev published a paper exploring its possibility. Building the thing was a tall order, requiring advances in a variety of fields that eventually had to be brought together in just the right way, but Microsoft knew that if it succeeded the payoff would be tremendous.

    This said, even if this wasn’t curiosity-driven research on Microsoft’s part, such research has already played a big role in both the company’s and the world’s fortunes. In the world’s fortune because, as with the work of Stoddart, Feringa, and Sauvage, the team explored, invented and/or refined new methods en route to building Majorana 1, methods which the rest of the world can potentially use to solve other problems. And in the company’s fortune because while Kitaev’s paper was motivated by the possibility of a device of considerable technological and commercial value, it drew from a large body of knowledge that — at the time it was unearthed and harmonised with the rest of science — wasn’t at all concerned with a quantum-computing chip in its then-distant future. For all its criticism, blue-sky research leads to some outcomes that no other forms of research can. This isn’t an argument in support of it so much as in defence of not sidelining it altogether.

    While I have many issues with how the Nobel Prizes are put together as an institution, I’ve covered each edition with not inconsiderable excitement[1]. Given the fondness of the prize-giving committee for work on or with artificial intelligence last year, it’s possible there’s a physics prize vouchsafed for work on the foundations of contemporary quantum computers in the not-too-distant future. When it comes to pass, I will be all too happy to fall back on the many pieces I’ve written on this topic over the years, to be able to confidently piece together the achievements in context and, personally, to understand the work beyond my needs as a journalist, as a global citizen. But until that day, I can’t justify the time I do spend reading up about and writing on this and similar topics as a journalist in a non-niche news publication — one publishing reports, analyses, and commentary for a general audience rather than those with specialised interests.

    The justification is necessary at all because the time I spend doing something is time spent not doing something else and the opportunity cost needs to be rational in the eyes of my employers. At the same time, journalism as a “history of now” would fail if it didn’t bring the ideas, priorities, and goals at play in the development of curiosity-driven research and — with the benefit of hindsight — its almost inevitable value for commerce and strategy to the people at large. This post so far, until this point, is the preamble I had in mind for my edition of The Hindu’s Notebook column today. Excerpt:

    It isn’t until a revolutionary new technology appears that the value of investing in basic research becomes clear. Many scientists are rooting for more of it. India’s National Science Day, today, is itself rooted in celebrating the discovery of the Raman effect by curiosity-driven study. The Indian government also wants such research in this age of quantum computing, renewable energy, and artificial intelligence. But it isn’t until such technology appears that the value of investing in a science journalism of the underlying research — slow-moving, unglamorous, not application-oriented — also becomes clear. It might even be too late by then.

    The scientific ideas that most journalists have overlooked are still very important: they’re the pillars on which the technologies reshaping the world stand. So it’s not fair that they’re overlooked when they’re happening and obscured by other concerns by the time they’ve matured. Without public understanding, input, and scrutiny in the developmental phase, the resulting technologies have fewer chances to be democratic, and the absence of the corresponding variety of journalism is partly to blame.

    I would have liked to include the preamble with the piece itself but the word limit is an exacting 620. This is also why I left something else unsaid in the piece, something important for me, the author, to have acknowledged. After the penultimate line — “You might think just the fact that journalists are writing about an idea should fetch it from the fringes to the mainstream, but it does not” — I wanted to say there’s a confounding factor: the skills, choices, and circumstances of the journalists themselves. If a journalist isn’t a good writer[2] or doesn’t have the assistance of good editors, what they write about curiosity-driven research, which already runs on weak legs among the people at large, may simply pass through their feeds and newsletters without inviting even a “huh?”. But as I put down the aforementioned line, a more discomfiting thought erupted at the back of my mind.

    In 2017, on the Last Word on Nothing blog, science journalist Cassandra Willyard made a passionate case for the science journalism of obscure things to put people at its centre in order to be effective. The argument’s allure was obvious but it has never sat well with me. The narrative power of human emotion, drawn from the highs or lows in the lives of the people working on obscure scientific ideas, is in being able to render those ideas more relatable. But my view is that there’s a lot out there we may never write about if we couldn’t also write about what highs/lows it rendered among its discoverers or beholders, and more so if such highs/lows don’t exist at all, as is often the case with a big chunk of curiosity-driven research. Willyard herself had used the then-recent example of the detection of gravitational waves from two neutron stars smashing into each other billions of lightyears away. This is conveniently (but perhaps not by her design) an example of Big Science where many people spent a long time looking for something and finally found it. There’s certainly a lot of drama here.

    But the reason I call having to countenance Willyard’s arguments discomfiting is that I understand what she’s getting at and I know I’m rebutting it on the back of only a small modicum of logic. It’s a sentimental holdout, even: I don’t want to have to care about the lives of other people when I know I care very well for how we extracted a world’s worth of new information by ‘reading’ gravitational waves emitted by a highly unusual cosmic event. The awe, to me, is right there. Yet I’m also keenly aware how impactful the journalism advocated by Willyard can be, having seen it in ‘action’ in the feature-esque pieces published by science magazines, where the people are front and centre, and the number of people that read and talk about them.

    I hold out because I believe there are, like me, many people out there (I’ve met a few) that can be awed by narratives of neutron-star collisions that dispense with invoking the human condition. I also believe that while a large number of people may read those feature-esque pieces, I’m not convinced they have a value that goes beyond storytelling, which is of course typically excellent. But I suppose those narratives of purely scientific research devoid of human protagonists (or antagonists) would have to be at least as excellent in order to captivate audiences just as well. If a journalist — together with the context in which they produce their work — isn’t up to the mark yet, they should strive to be. And this striving is essential if “you might think just the fact that journalists are writing about an idea should fetch it from the fringes to the mainstream, but it does not” is to be meaningful.


    [1] Not least because each Nobel Prize announcement is accompanied by three press releases: one making the announcement, one explaining the prize-winning work to a non-expert audience, and one explaining it in its full technical context. Journalism with these resources is actually quite enjoyable. This helps, too.

    [2] Im predominantly a textual journalist and default to write when writing about journalistic communication. But of course in this sentence I mean journalists who arent good writers and/or good video-makers or editors and/or good podcasters, etc.

  • A tale of vortices, skyrmions, paths and shapes

    There are many types of superconductors. Some of them can be explained by an early theory of superconductivity called Bardeen-Cooper-Schrieffer (BCS) theory.

    In these materials, vibrations in the atomic lattice force the electrons in the material to overcome their mutual repulsion and team up in pairs, if the material’s temperature is below a particular threshold (very low). These pairs of electrons, called Cooper pairs, have some properties that individual electrons can’t have. One of them is that all Cooper pairs together form an exotic state of matter called a Bose-Einstein condensate, which can flow through the material with much less resistance than individuals electrons experience. This is the gist of BCS theory.

    When the Cooper pairs are involved in the transmission of an electric current through the material, the material is an electrical superconductor.

    Some of the properties of the two electrons in each Cooper pair can influence the overall superconductivity itself. One of them is the orbital angular momentum, which is an intrinsic property of all particles. If both electrons have equal orbital angular momentum but are pointing in different directions, the relative orbital angular momentum is 0. Such materials are called s-wave superconductors.

    Sometimes, in s-wave superconductors, some of the electric current – or supercurrent – starts flowing in a vortex within the material. If these vortices can be coupled with a magnetic structure called a skyrmion, physicists believe they can give rise to some new behaviour previously not seen in materials, some of them with important applications in quantum computing. Coupling here implies that a change in the properties of the vortex should induce changes in the skyrmion, and vice versa.

    However, physicists have had a tough time creating a vortex-skyrmion coupling that they can control. As Gustav Bihlmayer, a staff scientist at the Jülich Research Centre, Germany, wrote for APS Physics, “experimental studies of these systems are still rare. Both parts” of the structures bearing these features “must stay within specific ranges of temperature and magnetic-field strength to realise the desired … phase, and the length scales of skyrmions and vortices must be similar in order to study their coupling.”

    In a new paper, a research team from Nanyang Technical University, Singapore, has reported that they have achieved just such a coupling: they created a skyrmion in a chiral magnet and used it to induce the formation of a supercurrent vortex in an s-wave superconductor. In their observations, they found this coupling to be stable and controllable – important attributes to have if the setup is to find practical application.

    A chiral magnet is a material whose internal magnetic field “typically” has a spiral or swirling pattern. A supercurrent vortex in an electrical superconductor is analogous to a skyrmion in a chiral magnet; a skyrmion is a “knot of twisting magnetic field lines” (source).

    The researchers sandwiched an s-wave superconductor and a chiral magnet together. When the magnetic field of a skyrmion in the chiral magnet interacted with the superconductor at the interface, it induced a spin-polarised supercurrent (i.e. the participating electrons’ spin are aligned along a certain direction). This phenomenon is called the Rashba-Edelstein effect, and it essentially converts electric charge to electron spin and vice versa. To do so, the effect requires the two materials to be in contact and depends among other things on properties of the skyrmion’s magnetic field.

    There’s another mechanism of interaction in which the chiral magnet and the superconductor don’t have to be in touch, and which the researchers successfully attempted to recreate. They preferred this mechanism, called stray-field coupling, to demonstrate a skyrmion-vortex system for a variety of practical reasons. For example, the chiral magnet is placed in an external magnetic field during the experiment. Taking the Rashba-Edelstein route means to achieve “stable skyrmions at low temperatures in thin films”, the field needs to be stronger than 1 T. (Earth’s magnetic field measures 25-65 µT.) Such a field could damage the s-wave superconductor.

    For the stray-field coupling mechanism, the researchers inserted an insulator between the chiral magnet and the superconductor. Then, when they applied a small magnetic field, Bihlmayer wrote, the field “nucleated” skyrmions in the structure. “Stray magnetic fields from the skyrmions [then] induced vortices in the [superconducting] film, which were observed with scanning tunnelling spectroscopy.”


    Experiments like this one reside at the cutting edge of modern condensed-matter physics. A lot of their complexity resides in scientists being able to closely control the conditions in which different quantum effects play out, using similarly advanced tools and techniques to understand what could be going on inside the materials, and to pick the right combination of materials to use.

    For example, the heterostructure the physicists used to manifest the stray-field coupling mechanism had the following composition, from top to bottom:

    • Platinum, 2 nm (layer thickness)
    • Niobium, 25 nm
    • Magnesium oxide, 5 nm
    • Platinum, 2 nm

    The next four layers are repeated 10 times in this order:

    • Platinum, 1 nm
    • Cobalt, 0.5 nm
    • Iron, 0.5 nm
    • Iridium, 1 nm

    Back to the overall stack:

    • Platinum, 10 nm
    • Tantalum, 2 nm
    • Silicon dioxide (substrate)

    The first three make up the superconductor, the magnesium oxide is the insulator, and the rest (except the substrate) make up the chiral magnet.

    It’s possible to erect a stack like this through trial and error, with no deeper understanding dictating the choice of materials. But when the universe of possibilities – of elements, compounds and alloys, their shapes and dimensions, and ambient conditions in which they interact – is so vast, the exercise could take many decades. But here we are, at a time when scientists have explored various properties of materials and their interactions, and are able to engineer novel behaviours into existence, blurring the line between discovery and invention. Even in the absence of applications, such observations are nothing short of fascinating.

    Applications aren’t wanting, however.


    quasiparticle is a packet of energy that behaves like a particle in a specific context even though it isn’t actually one. For example, the proton is a quasiparticle because it’s really a clump of smaller particles (quarks and gluons) that together behave in a fixed, predictable way. A phonon is a quasiparticle that represents some vibrational (or sound) energy being transmitted through a material. A magnon is a quasiparticle that represents some magnetic energy being transmitted through a material.

    On the other hand, an electron is said to be a particle, not a quasiparticle – as are neutrinos, photons, Higgs bosons, etc.

    Now and then physicists abstract packets of energy as particles in order to simplify their calculations.

    (Aside: I’m aware of the blurred line between particles and quasiparticles. For a technical but – if you’re prepared to Google a few things – fascinating interview with condensed-matter physicist Vijay Shenoy on this topic, see here.)

    We understand how these quasiparticles behave in three-dimensional space – the space we ourselves occupy. Their properties are likely to change if we study them in lower or higher dimensions. (Even if directly studying them in such conditions is hard, we know their behaviour will change because the theory describing their behaviour predicts it.) But there is one quasiparticle that exists in two dimensions, and is quite different in a strange way from the others. They are called anyons.

    Say you have two electrons in an atom orbiting the nucleus. If you exchanged their positions with each other, the measurable properties of the atom will stay the same. If you swapped the electrons once more to bring them back to their original positions, the properties will still remain unchanged. However, if you switched the positions of two anyons in a quantum system, something about the system will change. More broadly, if you started with a bunch of anyons in a system and successively exchanged their positions until they had a specific final arrangement, the system’s properties will have changed differently depending on the sequence of exchanges.

    This is called path dependency, and anyons are unique in possessing this property. In technical language, anyons are non-Abelian quasiparticles. They’re interesting for many reasons, but one application stands out. Quantum computers are devices that use the quantum mechanical properties of particles, or quasiparticles, to execute logical decisions (the same way ‘classical’ computers use semiconductors). Anyons’ path dependency is useful here. Arranging anyons in one sequence to achieve a final arrangement can be mapped to one piece of information (e.g. 1), and arranging anyons by a different sequence to achieve the same final arrangement can be mapped to different information (e.g. 0). This way, what information can be encoded depends on the availability of different paths to a common final state.

    In addition, an important issue with existing quantum computers is that they are too fragile: even a slight interaction with the environment can cause the devices to malfunction. Using anyons for the qubits could overcome this problem because the information stored doesn’t depend on the qubits’ existing states but the paths that they have taken there. So as long as the paths have been executed properly, environmental interactions that may disturb the anyons’ final states won’t matter.

    However, creating such anyons isn’t easy.

    Now, recall that s-wave superconductors are characterised by the relative orbital angular momentum of electrons in the Cooper pairs being 0 (i.e. equal but in opposite directions). In some other materials, it’s possible that the relative value is 1. These are the p-wave superconductors. And at the centre of a supercurrent vortex in a p-wave superconductor, physicists expect to find non-Abelian anyons.

    So the ability to create and manipulate these vortices in superconductors, as well as, more broadly, explore and understand how magnet-superconductor heterostructures work, is bound to be handy.


    The Nanyang team’s paper calls the vortices and skyrmions “topological excitations”. An ‘excitation’ here is an accumulation of energy in a system over and above what the system has in its ground state. Ergo, it’s excited. A topological excitation refers to energy manifested in changes to the system’s topology.

    On this subject, one of my favourite bits of science is topological phase transitions.

    I usually don’t quote from Wikipedia but communicating condensed-matter physics is exacting. According to Wikipedia, “topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending”. For example, no matter how much you squeeze or stretch a donut (without breaking it), it’s going to be a ring with one hole. Going one step further, your coffee mug and a donut are topologically similar: they’re both objects with one hole.

    I also don’t like the Nobel Prizes but some of the research that they spotlight is nonetheless awe-inspiring. In 2016, the prize was awarded to Duncan Haldane, John Kosterlitz and David Thouless for “theoretical discoveries of topological phase transitions and topological phases of matter”.

    David Thouless in 1995. Credit: Mary Levin/University of Washington

    Quoting myself from 2016:

    There are four popularly known phases of matter: plasma, gas, liquid and solid. If you cooled plasma, its phase would transit to that of a gas; if you cooled gases, you’d get a liquid; if you cooled liquids, you’d get a solid. If you kept cooling a solid until you were almost at absolute zero, you’d find substances behaving strangely because, suddenly, quantum mechanical effects show up. These phases of matter are broadly called quantum phases. And their phase transitions are different from when plasma becomes a gas, a gas becomes a liquid, and so on.

    A Kosterlitz-Thouless transition describes a type of quantum phase transition. A substance in the quantum phase, like all substances, tries to possess as low energy as possible. When it gains some extra energy, it sheds it. And how it sheds it depends on what the laws of physics allow. Kosterlitz and Thouless found that, at times, the surface of a flat quantum phase – like the surface of liquid helium – develops vortices, akin to a flattened tornado. These vortices always formed in pairs, so the surface always had an even number of vortices. And at very low temperatures, the vortices were always tightly coupled: they remained close to each other even when they moved across the surface.

    The bigger discovery came next. When Kosterlitz and Thouless raised the temperature of the surface, the vortices moved apart and moved around freely, as if they no longer belonged to each other. In terms of thermodynamics alone, the vortices being alone or together wouldn’t depend on the temperature, so something else was at play. The duo had found a kind of phase transition – because it did involve a change in temperature – that didn’t change the substance itself but only a topological shift in how it behaved. In other words, the substance was able to shed energy by coupling the vortices.

    Reality is so wonderfully weird. It’s also curious that some concepts that seemed significant when I was learning science in school (like invention versus discovery) and in college (like particle versus quasiparticle) – concepts that seemed meaningful and necessary to understand what was really going on – don’t really matter in the larger scheme of things.